Question

which equation shows the distributive property of multiplication?
2 × 7 − 2 × 4 = 2 × (7 − 4)
5 = 1 × 5
(4 × 7) × 1 = 4 × (7 × 1)
0 × 3 = 0

Explanation:

Step1: Recall Distributive Property

The distributive property of multiplication over subtraction is \(a\times b - a\times c = a\times(b - c)\), and over addition is \(a\times b + a\times c = a\times(b + c)\).

Step2: Analyze Each Option

• Option 1: \(2\times7 - 2\times4 = 2\times(7 - 4)\) matches the distributive property \(a\times b - a\times c = a\times(b - c)\) (here \(a = 2\), \(b = 7\), \(c = 4\)).
• Option 2: \(5 = 1\times5\) is the identity property of multiplication (any number times 1 is itself).
• Option 3: \((4\times7)\times1 = 4\times(7\times1)\) is the associative property of multiplication (changing grouping of factors).
• Option 4: \(0\times3 = 0\) is the zero property of multiplication (any number times 0 is 0).

Answer:

\(2\times7 - 2\times4 = 2\times(7 - 4)\) (the first equation)